SEE2030: Introduction to Computer Systems (Fall 2017) Programming Assignment #2:

Transcription

1 SEE2030: Introduction to Computer Systems (Fall 2017) Programming Assignment #2: Implementing Arithmetic Operations using the Tiny FP (8-bit floating point) representation Due: October 15th (Sunday), 11:59PM 1. Introduction The purpose of this assignment is to implement several arithmetic operations using the simplified 8-bit floating-point type. 2. Problem specification 2.1. Overview tinyfp is a simplified 8-bit floating point representation which follows the IEEE 754 standard for floating-point arithmetic. The overall structure of the tinyfp representation is shown below. The MSB (Most Significant Bit) is used as a sign bit (s). The next four bits are used for exponents (exp) with a bias value of 7. The last three bits are used for the fractional part (frac). In C, the new type tinyfp can be defined as follows. typedef unsigned char tinyfp; Your task is to implement the following four C functions that operate using the tinyfp data type. tinyfp add(tinyfp tf1, tinyfp tf2); tinyfp mul(tinyfp tf1, tinyfp tf2); int gt(tinyfp tf1, tinyfp tf2); int eq(tinyfp tf1, tinyfp tf2);

2 2.2. Restrictions You must not use any float-type or double-type variables for implementing functions introduced above. Also, you should not use the conversion functions such as tinyfp2float() implemented in PA#1. You should implement these functions using 32-bit integer arithmetic and logical operations Implementation details Common - We do not differentiate between +NaN and -NaN. They are all treated as NaN. e.g. ( ) tinyfp == ( ) tinyfp == NaN - Also note that +0 and -0 are same by definition. The all mean the value zero tinyfp add(tinyfp tf1, tinyfp tf2) - If the result exceeds the range of the tinyfp representation, the result will be infinity (+ or - depending on the sign). - Use the round-to-even mode when necessary. - For the special cases which involve infinity and NaN, add() should return the value specified in Table 1. Table 1. Return values of add() for special values + Normalized/Denormalized + - Normalized/Denormalized - Normalized/Denormalized + + Normalized/Denormalized NaN - + NaN NaN Anything NaN Anything NaN NaN

3 tinyfp mul(tinyfp tf1, tinyfp tf2) - If the result exceeds the range of tinyfp representation, the result will be infinity (+ or - depending on the sign). - Use the round-to-even mode when necessary. - For the special cases which involve infinity and NaN, mul() should return the value specified in Table 2. Table 2. Return value of mul() for special values ± Normalized/Denormalized ± (depending on the sign of tf1 and tf2) Normalized/Denormalized ± ± (depending on the sign of tf1 and tf2) ± ±0 NaN ±0 ± NaN NaN Anything NaN Anything NaN NaN

4 int gt(tinyfp tf1, tinyfp tf2) - Return 1 if tf1 is greater than tf2. Otherwise, return 0. - For the special cases which involve infinity and NaN, gt() should return the value specified in Table 3. Table 3. Return value of gt() for special values + Normalized/Denormalized 1 Normalized/Denormalized Normalized/Denormalized 0 Normalized/Denormalized Anything NaN 0 NaN Anything 0

5 int eq(tinyfp tf1, tinyfp tf2) - Return 1 if tf1 and tf2 are equal. Otherwise, return 0. - For the special cases which involve infinity and NaN, eq() should return the value specified in Table 4. Table 4. Return value of eq() for special values NaN Anything 0 Anything NaN 0

6 3. Example The skeleton code is available in the course homepage ( The results of some sample runs are as follows. 4. Hand in instructions Submit only the pa2.c file to the submission site.

7 5. Logistics You will work on this assignment alone. We will also measure the speed of your program. The correct solutions with fast running time will have the bonus. Only the assignments submitted before the deadline will receive the full credit. 25% of the credit will be deducted for every single day delay. You can use up to 5 slip days Any attempt to copy others work will result in heavy penalty (for both the copier and the originator). Don t take a risk. Good luck! TA: Kisik Jeong (kisik.jeong@csl.skku.edu) Computer Systems Laboratory Sungkyunkwan University